You need the moderate wing, in effect the old Progressive strain of the GOP to remain firmly in control, the Democratic big tent needs to fold and revert to its traditional hold in South. This GOP should be generally socially conservative but more progressive on civil rights generally, the Democrats likely fall into more populist swings, steering socially conservative and less civil rights minded. The GOP will be economically Liberal minded while the Democrats might indulge in popular social welfare to garner votes thus not fully Liberal in a classical sense, they play more to conservative minded GOP voters in the Midwest but might lose the progressive West and industrial North if Republicans stay in favor of unions. Civil rights should get you the women's rights and breakdown of Jim Crow, neither party is going to embrace sexual liberalization. Your bigger challenge is the birth control pill, it revolutionized sex for women by taking pregnancy out of the equation. But does that mean all the social morays are dead? One might argue that a stronger feminist argument in civil rights argues for sexual "equality" but one can see how it may never argue for sexual "freedom." Take away the turmoil of Vietnam, have the prosperity bubble last longer to shift more Americans to staid suburban life and middle-class notions of good behavior and this might be how America behaves. Doable but I think it is better to reach back before 1950 to seed the trends you need.